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Congruences on free monoids and submonoids of polycyclic monoids

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

John Meakin  and
Mark Sapir
John Meakin
Affiliation:
Department of Mathematics and StatisticsUniversity of Nebraska-LincolnLincoln, Nebraska 68588-0323, U.S.A.
Mark Sapir
Affiliation:
Department of Mathematics and StatisticsUniversity of Nebraska-LincolnLincoln, Nebraska 68588-0323, U.S.A.
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Abstract

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We establish a one-to-one “group-like” correspondence between congruences on a free monoid X* and so-called positively self-conjugate inverse submonoids of the polycyclic monoid P(X). This enables us to translate many concepts in semigroup theory into the language of inverse semigroups.

MSC classification

Secondary: 20M10: General structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 2 , April 1993 , pp. 236 - 253
Copyright
Copyright © Australian Mathematical Society 1993

References

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